Deconvolution for the reduction of blurring induced by internal reflections

ABSTRACT

A system and method of image processing employ mathematical deconvolution to estimate the magnitude and location of a target object within an image. Both the nature of internal reflections and the convolution process by which each internal reflection contributes to blurring of the acquired image data may be measured and modeled. In accordance with mathematical deconvolution techniques, the combined effects of these internal reflections may be reduced to the extend that respective contributions of the target object and each individual reflection may be distinguished and quantified.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of application Ser. No.10/742,508, filed Dec. 19, 2003, which claims the benefit of U.S.provisional application Ser. No. 60/437,264, filed Dec. 31, 2002.

FIELD OF THE INVENTION

Aspects of the present invention relate generally to digital imageprocessing techniques, and more particularly to an image processingsystem and method employing mathematical deconvolution to estimate therespective magnitudes and locations of objects within an image.

DESCRIPTION OF THE RELATED ART

Digital imaging systems have been well described in the art. In general,these systems typically comprise some or all of the followingcomponents: a sample support mechanism for supporting a sample orspecimen to be imaged; an illumination source providing excitation lightto illuminate the sample; an optical train operative to focus an imageof the sample and to provide enlargement, magnification, resolutionenhancement, and other optical effects; a detector or other imagingapparatus such as a charge-coupled device (CCD) camera or acomplementary metal oxide semiconductor (CMOS) sensor device, forexample; and a computer system or other control apparatus for acquiring,storing, and displaying the images collected by the detector.

The quality of images collected in a conventional manner by typicalsystems is often affected by internal reflections associated with thesample support, the optical train, the detector, or some combination ofthese components. Images of large, bright objects tend to be surroundedby regions of decreased contrast; these peripheral regions generallyappear as halos of reduced contrast in the final image. Moreover,individual halos from a number of discrete bright objects may sum toreduce the overall contrast of the image further. Even whenanti-reflective coatings and non-parallel optical surfaces are employedin efforts to minimize contrast degradation, these halos may persist. Inparticular, the halos or contrast reduction attributable to the samplesupport and the optical coatings of the detector itself may beparticularly difficult to eliminate.

Conventional technology is deficient at least to the extent that thequality of acquired images may be degraded by indispensable componentsof the image system itself, such as the detector and various opticalelements as set forth above. What is needed is a system and method tominimize the deleterious effects of internal reflections associated withthe sample support, the optical train, and the detector on overall imagequality in digital image acquisition and processing applications.

SUMMARY

Embodiments of the present invention overcome the above-mentioned andvarious other shortcomings of conventional technology, providing asystem and method of image processing which employ mathematicaldeconvolution to estimate the respective magnitudes and locations ofobjects within an image.

In accordance with one exemplary embodiment, a method comprises:acquiring image data of a target object; modeling the image data tocreate modeled data; responsive to the modeling, estimating a size andan intensity of an internal reflection in an optical train; anddeconvolving the modeled data in accordance with the estimating.

The modeling may comprise mathematically expressing the modeled data asa sum of object data representing the target object and reflection datarepresenting the internal reflection. In that regard, some modeling inaccordance with the present disclosure further comprises mathematicallyexpressing the reflection data as a plurality of factors, wherein eachof the plurality of factors is associated with a respective internalreflection. The estimating may comprise utilizing a series ofcylindrical functions; additionally or alternatively, the estimating maycomprise utilizing a series of Bessel functions or Gaussian functions.

One exemplary method may further comprise estimating a magnitude and alocation of the target object in accordance with the deconvolving. Insome embodiments described herein, the method further comprisesestimating a magnitude and a location of the target object using theobject data (from the modeling operation, for example) and in accordancewith the deconvolving.

The acquiring generally comprises utilizing an imaging apparatus, suchas a charge-coupled device or a complementary metal oxide semiconductorsensor device. Additional embodiments further comprise storing finalimage data in accordance with the deconvolving, displaying final imagedata in accordance with the deconvolving, or both.

An embodiment of a computer readable medium encoded with data andcomputer executable instructions for processing image data representinga target object is also contemplated. It will be appreciated that theimage data in such embodiments is generally acquired from an imagingsystem. In embodiments operative in accordance with the presentdisclosure, the data and instructions cause an apparatus executing theinstructions to: model the image data to create modeled data; estimate asize and an intensity of an internal reflection in an optical train ofthe imaging system using the modeled data; and deconvolve the modeleddata using results of the estimating operation.

The computer readable medium may be further encoded with data andcomputer executable instructions causing an apparatus executing theinstructions to express the modeled data mathematically as a sum ofobject data representing the target object and reflection datarepresenting the internal reflection. As with the method embodimentdescribed above, an apparatus executing the instructions may express thereflection data mathematically as a plurality of factors, wherein eachof the plurality of factors is associated with a respective internalreflection.

The computer readable medium may be further encoded with data andcomputer executable instructions causing an apparatus executing theinstructions to perform the estimating operation utilizing a series ofcylindrical functions, Bessel functions, Gaussian functions, or somecombination thereof.

The computer readable medium may be further encoded with data andcomputer executable instructions causing an apparatus executing theinstructions to estimate a magnitude and a location of the target objectusing results of the deconvolving operation. Such an estimate may useobject data as noted above with reference to the method embodiment.

The computer readable medium may be further encoded with data andcomputer executable instructions causing an apparatus executing theinstructions to store final image data resulting from the deconvolvingoperation, display final image data resulting from the deconvolvingoperation, or both.

The foregoing and other aspects of various embodiments of the presentinvention will be apparent through examination of the following detaileddescription thereof in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a simplified functional block diagram illustrating componentsof a digital image acquisition and processing system with whichembodiments of a mathematical deconvolution method may be employed.

FIG. 1B is a simplified functional block diagram illustrating a portionof the image acquisition and processing system depicted in FIG. 1A.

FIG. 2 is a simplified flow diagram illustrating the general operationof one embodiment of an image processing method employing mathematicaldeconvolution.

DETAILED DESCRIPTION

Aspects of the present invention relate to deconvolving digital images.In operation of a typical imaging system, the individual halosattributable to respective internal reflections become convolved withthe true image of the object, inducing an effect that appears asblurring in the image. The convolution process and the nature of theseinternal reflections may be measured and modeled; the combined effectsof the reflections may then be reduced through a process of mathematicaldeconvolution as set forth in more detail below. Image data processed inaccordance with the present disclosure may more accurately represent theactual objects, intensities, and distributions than the original imagedata acquired by the imaging system.

Turning now to the drawing figures, FIG. 1A is a simplified functionalblock diagram illustrating components of a digital image acquisition andprocessing system with which embodiments of a mathematical deconvolutionmethod may be employed, and FIG. 1B is a simplified functional blockdiagram illustrating a portion of the image acquisition and processingsystem depicted in FIG. 1A. Those of skill in the art will appreciatethat FIGS. 1A and 1B are provided by way of example only, and that thespecific arrangement of components is susceptible of numerousmodifications; the exemplary scale, orientation, and interrelationshipof the various components may be altered in accordance with systemrequirements. Additionally, as will become apparent from examination ofthe following description, some or all of the functionality of somecomponents depicted as discrete elements may be combined or incorporatedinto other components.

As illustrated in FIGS. 1A and 1B, system 100 generally comprises amicroscope 110 operably coupled to a sample support mechanism, typicallyembodied in a precision movable stage 120, and to an image acquisitioncomponent 140. Stage 120 may be configured and operative to support amicroarray, microscope slide, or other similar structure (referencenumeral 190) upon which a specimen or target object 199 to be imaged isdisposed. As is generally known in the art, microscope 110 may comprise,or be operative in conjunction with, an illumination source 111 forilluminating state 120, slide 190, or both with light of a predeterminedor selected frequency or spectral bandwidth; in that regard,illumination source 111 may provide light in the visible, infrared, orultraviolet wavelengths.

In some embodiments, illumination source 111 may be incorporated withinhousing 112 of microscope 110, i.e., on the opposite side of stage 120and slide 190 than depicted in FIG. 1A. Alternatively, an additionalsource of illumination (not shown) to be used in conjunction with, or inlieu of, source 111 may be accommodated or maintained in housing 112. Inthese embodiments, any such illumination source disposed within housing112 may be suitable dimensioned and positioned neither to interfere withoptical components of microscope 110 nor to obstruct the optical paththrough microscope 110 (to image acquisition component 140).

Stage 120 may be movable relative to optics (e.g., objective 119illustrated in FIG. 1B) incorporated into microscope 110 (microscopeoptics are not depicted in FIG. 1A). In some embodiments, stage 120 maybe movable in both the x and y directions (where the y axis is normal tothe plane of FIG. 1A). Additionally or alternatively, stage 120 mayincorporate or comprise one or more structures and mechanisms configuredand operative precisely to position slide 190 in the x and y directionsrelative to the structure of stage 120 itself. In such embodiments,precise two-dimensional positioning (i.e., x and y coordinates) ofobject 199 relative to the optical path of microscope 110 may beachieved through movement of stage 120 relative to microscope optics,movement of slide 190 relative to stage 120, or both.

In some embodiments, stage 120 may also be movable along the z axis (theoptical axis). It will be appreciated that microscope optics may alsofacilitate positioning an object on slide 190 in the proper location inthree-dimensional space (i.e., x, y, and z coordinates) relative to theoptical path and the focal point of objective 119. In that regard, oneor more optical components of microscope 110 such as objective 119 maybe movable in the z direction, either in addition to, or as analternative to, selectively moving stage 120 along the optical axis.Additionally or alternatively, objective 119 may be movable along the xaxis, the y axis, or both.

It will be appreciated that numerous mechanism and methods ofpositioning object 199 to be imaged relative to microscope optics aregenerally known. Relative movement of various components (such as slide190, stage 120, and objective 119, for example), either individually orin combination, may vary in accordance with system requirements andconfiguration, and may be effectuated to position object 199 in asuitable location relative to objective 119. The present disclosure isnot intended to be limited by the structures and processes employed toposition object 199 relative to objective 119 and the optical path.

Microscope optics may generally be configured and operative inconjunction with image acquisition component 140; in that regard,component 140 generally comprises a camera, a charge-coupled device(CCD) sensor apparatus, a complementary metal oxide semiconductor (CMOS)sensor device, or other detector 141 operably coupled to an imageprocessor 142 or other appropriate electronics. System 100 mayadditionally include control electronics 150 operative to control, forexample: operational parameters, functional characteristics, or otherconfigurable aspects of image processor 142 and detector 141; two- orthree-dimensional motion of stage 120, objective 119, or othercomponents; power output, spectral bandwidth, frequencies, or otheroperational parameters of source 111 and any other illumination source;data storage; and the like. In that regard, electronics 150 may compriseone or more microprocessors, microcontrollers, or other programmabledevices capable of executing computer readable instructions;additionally, electronics 150 may also comprise or be operably coupledwith data storage media. Those of skill in the art will appreciate thatvarious methods and apparatus employing microprocessors or computerexecutable instruction sets to configure and to control operation ofimage acquisition systems are generally known.

During operation of system 100, image data acquired by detector 141 maybe summed, manipulated, saved, or otherwise processed by hardware,software, or both resident at image processor 142; in some embodiments,functionality of processor 142 may be influenced or controlled bysignals transmitted from electronics 150 as noted above. Alternatively,the functionality of image processor 142 and electronics 150 may beincorporated into a single device, for example. Specifically, imageprocessor 142 may be operative in accordance with instruction sets tocompute solutions or approximations for the equations set forth below.

The image collected by an optical system (e.g., such as detector 141 andimage processor 142 in FIG. 1A) may be described as a combination ofimage data representing the actual target object plus image datarepresenting the combined effects of individual internal reflectionsattributable to various system components. Each internal reflection, inturn, may be described as a cylindrical step function of some magnitudeand width. This may be described mathematically as follows:

$\begin{matrix}{I_{image} = {\Theta_{object} + {{\Theta_{object} \otimes P_{a}}{\Pi_{a}\left( \frac{r}{2a} \right)}} + {{\Theta_{object} \otimes P_{b}}{\Pi_{b}\left( \frac{r}{2b} \right)}} + {\ldots \mspace{14mu} {\Theta_{object} \otimes P_{x}}{\Pi_{x}\left( \frac{r}{2x} \right)}}}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$

As set forth in Equation 1 above, the image (I_(image)) may be formed bysumming the contribution of the target object (Θ_(object)) andcontributions of that target object convolved

with a series of cylindrical functions (Π_(x)) having a peak height ofP_(x) and a width of 2x, where x is the radius and r is the distancefrom the center of Π_(x). The peak of each of these functions may bedetermined or influenced by the magnitude of the respective internalreflection each function represents; the width may be defined orinfluenced by the location of the respective internal reflection withinthe optical train, as well as by the overall magnification of theoptical trains.

Solving for Θ and omitting scaling factors, P_(x,) produces

I=Θ+Θ

[Π _(a)+Π_(b)+ . . . Π_(x)]  (Eq. 2)

Solving for the original target object (Θ_(object)) yields

Θ=I−Θ

[Π _(a)+Π_(b)+ . . . Π_(x)]  (Eq. 3)

Taking the Fourier Transform of both sides of Equation 3 yields thefollowing:

F[Θ]=F{I−Θ

[Π _(a)+Π_(b)+ . . . Π_(x) ]}=F[I]−F[Θ]F[Π _(a)+Π_(b)+ . . .Π_(x)]  (Eq. 4)

Solving for F[I]:

F[I]=F[Θ]+F[Θ]F[Π _(a)+Π_(b)+ . . . Π_(x)]  (Eq. 5)

Solving now for F[Θ]:

$\begin{matrix}{{F\lbrack\Theta\rbrack} = \frac{F\lbrack I\rbrack}{1 + {F\left\lbrack {\Pi_{a} + \Pi_{b} + {\ldots \mspace{14mu} \Pi_{x}}} \right\rbrack}}} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$

Inverse Fourier Transformation yields Equation 7 as set forth below:

$\begin{matrix}{\Theta = {F^{- 1}\left\{ \frac{F\lbrack I\rbrack}{1 + {F\left\lbrack {\Pi_{a} + \Pi_{b} + {\ldots \mspace{14mu} \Pi_{x}}} \right\rbrack}} \right\}}} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$

From Integral Tables published in the art, the Fournier transform ofΠ_(x) may be expressed as follows:

$\begin{matrix}{{F\left\lbrack {\Pi \left( \frac{r}{2a} \right)} \right\rbrack} = \frac{{aJ}_{1}\left( {2\pi \; {aq}} \right)}{q}} & \left( {{Eq}.\mspace{14mu} 8} \right)\end{matrix}$

where J₁ is a first order Bessel Function and q is spatial frequency.Expanding, now, for the solution to Θ and including scaling factors,P_(x):

$\begin{matrix}{\Theta = {F^{- 1}\left\{ \frac{F\lbrack I\rbrack}{\begin{matrix}{1 + {P_{a}\left\lbrack \frac{{aJ}_{1}\left( {2\pi \; {aq}} \right)}{q} \right\rbrack} +} \\{{P_{b}\left\lbrack \frac{{bJ}_{1}\left( {2\pi \; {bq}} \right)}{q} \right\rbrack} + {\ldots \mspace{14mu} {P_{x}\left\lbrack \frac{{xJ}_{1}\left( {2\pi \; {xq}} \right)}{q} \right\rbrack}}}\end{matrix}} \right\}}} & \left( {{Eq}.\mspace{14mu} 9} \right)\end{matrix}$

Optical modeling software and empirical measurements may be used tosolve for the magnitude and size of the contribution from each opticalinterface. these contributions can then be used to solve for Θ using theFourier method set forth above.

FIG. 2 is a simplified flow diagram illustrating the general operationof one embodiment of an image processing method employing mathematicaldeconvolution. As indicated at block 211, an exemplary image processingmethod may acquire image data of an appropriately illuminated targetobject. The acquiring operation depicted at block 211 may compriseutilization of an embodiment of an image acquisition system such as setforth in detail above with reference to FIGS. 1A and 1B. In someimplementations, microscope optics may be configured and operative inconjunction with an image acquisition component such as a camera, a CCDor CMOS sensor device, or other detector operably coupled to an imageprocessor or other appropriate electronics. It will be appreciated thatsuch image acquisition systems may be susceptible of numerousalternations, and that neither the present disclosure, in general, northe acquiring operation at block 211 in FIG. 2, in particular, isintended to be limited by the specific components and functionalcharacteristics of any particular image acquisition system.

Acquired image data may be modeled (to create “modeled data”) asindicated at block 212. As set forth above, the image collected by anoptical system (e.g., the “image data” acquired at block 211) may bedescribed as a combination of data representing the actual target objectplus data representing individual internal reflections attributable tovarious system components. In that regard, one embodiment of themodeling at block 212 may generally comprise mathematically expressing“modeled data” as a sum of “object data,” which represents thecontribution of the target object, and “reflection data,” whichrepresents the contribution of an internal reflection. This mathematicalsummation approach to the modeling operation 212 is represented at block221 in FIG. 2.

As set forth in Equation 1 and described above, exemplary modeling atblock 212 may consider the contribution of the target object(Θ_(object)) and contributions of that target object convolved

with a series of cylindrical functions (Π_(x)). It will be appreciated,however, that various other functions (i.e., not cylindrical stepfunctions) may be used in lieu of, or in addition to, Π_(x) in Equation1 or in other modeling strategies. For example, Gaussian or Bessel typefunctions may also be used to model the internal reflections.

Responsive to the modeling at block 212 (and, depending on theembodiment, the summing at block 221), a size and an intensity of aninternal reflection in an optical train of the imaging system may beestimated as indicated at block 213. As set forth above, such internalreflections may be attributable to mechanical components (such as thestage or sample support apparatus) and optical components (such as theimaging device or optics) of the image acquisition system. Additionally,more than one internal reflection may contribute to the halo effect thatcauses blurring as described above. Accordingly, the modeling (block212), summing (block 221), and estimating (block 213) may account formultiple internal reflections. In some such embodiments, for example,the modeling operation at block 212 may further comprise mathematicallyexpressing the reflection data as a plurality of factors, each of whichmay be associated with a respective internal reflection. The pluralityof factors may be summed at block 221 and estimated at block 213 toaccount for the contribution of each respective internal reflection increation of the modeled data.

In accordance with some embodiments, a table, array, or other datastructure may be implemented to store specific reflection parameters(e.g., such as P_(x) and x in Equation 1) for a particular configurationof optical components. The number and nature of such stored parametersmay be influenced by the type of functions (e.g., such as Π_(x) inEquation 1) used to model the internal reflections. If specific valuesfor appropriate parameters are maintained in a fixed or static datastructure accessible, for example, by deconvolution software or othercomputer executable instruction sets, the modeling operation at block212 and the estimating operation at block 213 (as these relate tointernal reflections attributable to components of the imaging system)may be performed only when particular optical components of the imagingsystem arc changed or modified.

Modeled data may be deconvolved as indicated at block 214. From theforegoing detailed description, it will be appreciated that thedeconvolution of modeled data at block 214 may be performed inaccordance with the estimating at block 213. In that regard, someembodiments of the estimating at block 213 may comprise utilizing orimplementing a series of cylindrical functions such as described abovewith reference to Equation 1. Deconvolving at block 214 may distinguishand quantify contributions (to the acquired “image data”) attributableto the target object from contributions attributable to one or moreinternal reflections.

Specifically, as indicated at block 215, the magnitude and location ofthe target object may be estimated in accordance with the deconvolvingat block 214. As noted above, such estimating at block 215 may compriseusing the “object data” (i.e., a subset of the acquired “image data”)identified at blocks 212 and 221.

As indicated at block 216, the exemplary image processing method of FIG.2 may further comprise storing “final image data,” such as by writingthese data to a memory device. Examples of suitable storage devicesinclude a digital versatile disk (DVD) or compact disk (CD) driveapparatus, for example; other types of media and electronic hardwaredevices for storing data are generally known in the art. Additionally oralternatively, final image data may be sent to a monitor (e.g., a liquidcrystal display (LCD) or cathode ray tube (CRT) display), transmittedvia network connection to one or more computer terminals or servers, orboth.

The “final image data” referenced in block 216 may be created inaccordance with the deconvolving at block 214 and the estimating atblock 215. Specifically, in accordance with the FIG. 2 embodiment, boththe nature of the internal reflections and the convolution process bywhich each internal reflection contributes to blurring of the acquiredimage data may be measured and modeled. In accordance with thedeconvolving (block 214) and estimating (block 215), the combinedeffects of these internal reflections may be reduced in the final imagedata written, saved, displayed, or some combination thereof (block 216)to the extent that respective contributions of the target object andeach individual reflection may be distinguished and quantified.Accordingly, object data and reflection data contributing to the finalimage data may be expressed as constituent parts, as indicated at block222.

Various alternatives exist with respect to the FIG. 2 embodiment, andthe presented order of the individual blocks is not intended to imply aspecific sequence of operations to the exclusion of other possibilities.Specifically, the particular application and overall system requirementsmay dictate the most efficient or desirable sequence of the operationsset forth in FIG. 2. Individual operations depicted at discrete blocks(such as, for example, the modeling and summing at blocks 212 and 221)may be integrated or combined, for example, where appropriatemathematical operations, computer software routines, or both, are to beimplemented.

Though not limited with respect to particular context andimplementations, the foregoing embodiments or modified versions thereofmay have specific utility in conjunction with strategies or techniquesfor imaging biomedical samples or specimens. By way of example, suchtechniques include methods of acquiring and processing two-dimensionalimages of biochips, microarrays, and histological specimens.Additionally or alternatively, the foregoing functionality may beemployed in conjunction with methods of acquiring and processingindividual two-dimensional images of multi-dimensional series of imagesacquired, for example, across different axial locations, differentcolors or wavelengths, different successive time points, and differentimaging modalities. The foregoing list is not intended to be exhaustive;other practical applications of mathematical deconvolution as set forthherein are contemplated.

Several features and aspects of the present invention have beenillustrated and described in detail with reference to particularembodiments by way of example only, and not by way of limitation. Thoseof skill in the art will appreciate that alternative implementations andvarious modifications to the disclosed embodiments are within the scopeand contemplation of the present disclosure. Therefore, it is intendedthat the invention be considered as limited only by the scope of theappended claims.

1. A method comprising: acquiring image data of a target object;modeling said image data to create modeled data; responsive to saidmodeling, estimating a size and an intensity of an internal reflectionin an optical train; and deconvolving said modeled data in accordancewith said estimating.
 2. The method of claim 1 wherein said modelingcomprises mathematically expressing said modeled data as a sum of objectdata representing said target object and reflection data representingsaid internal reflection.
 3. The method of claim 2 wherein said modelingfurther comprises mathematically expressing said reflection data as aplurality of factors, wherein each of said plurality of factors isassociated with a respective internal reflection.
 4. The method of claim1 wherein said estimating comprises utilizing a series of cylindricalfunctions.
 5. The method of claim 1 further comprising estimating amagnitude and a location of said target object in accordance with saiddeconvolving.
 6. The method of claim 2 further comprising estimating amagnitude and a location of said target object using said object dataand in accordance with said deconvolving.
 7. The method of claim 1wherein said acquiring comprises utilizing a charge-coupled device. 8.The method of claim 1 wherein said acquiring comprises utilizing acomplementary metal oxide semiconductor sensor device.
 9. The method ofclaim 1 further comprising storing final image data in accordance withsaid deconvolving.
 10. The method of claim 1 further comprisingdisplaying final image data in accordance with said deconvolving.
 11. Acomputer readable medium encoded with data and computer executableinstructions for processing image data representing a target object;said image data acquired from an imaging system; the data andinstructions causing an apparatus executing the instructions to: modelsaid image data to create modeled data; estimate a size and an intensityof an internal reflection in an optical train of said imaging systemusing said modeled data; and deconvolve said modeled data using resultsof the estimating operation.
 12. The computer readable medium of claim11 further encoded with data and computer executable instructions; thedata and instructions further causing an apparatus executing theinstructions to express said modeled data mathematically as a sum ofobject data representing said target object and reflection datarepresenting said internal reflection.
 13. The computer readable mediumof claim 12 further encoded with data and computer executableinstructions; the data and instructions further causing an apparatusexecuting the instructions to express said reflection datamathematically as a plurality of factors, wherein each of said pluralityof factors is associated with a respective internal reflection.
 14. Thecomputer readable medium of claim 11 further encoded with data andcomputer executable instructions; the data and instructions furthercausing an apparatus executing the instructions to perform saidestimating operation utilizing a series of cylindrical functions. 15.The computer readable medium of claim 11 further encoded with data andcomputer executable instructions; the data and instructions furthercausing an apparatus executing the instructions to estimate a magnitudeand a location of said target object using results of the deconvolvingoperations.
 16. The computer readable medium of claim 12 further encodedwith data and computer executable instructions, the data andinstructions further causing an apparatus executing the instructions toestimate a magnitude and a location of said target object using saidobject data and results of the deconvolving operation.
 17. The computerreadable medium of claim 11 further encoded with data and computerexecutable instructions; the data and instructions further causing anapparatus executing the instructions to store final image data resultingfrom the deconvolving operation.
 18. The computer readable medium ofclaim 11 further encoded with data and computer executable instructions;the data and instructions further causing an apparatus executing theinstructions to display final image data resulting from the deconvolvingoperations.
 19. The computer readable medium of claim 11, wherein thetarget object is mounted on a stage that is movable relative to theoptical train.
 20. The method of claim 1, wherein the target object ismounted on a stage that is movable relative to the optical train.